Colin Kaepernick and other National Football League players are doing what Saul Alinsky, founder of the Industrial Areas Foundation, often advised: They are engaging in public action and achieving the first goal of any action—generating reactions. The most important and fundamental reaction is recognition: See us. Hear us. And once you’ve done that, recognize our cause.

The problem is that they are not taking the next step, which is to get into a public relationship so that a real exchange of views can occur and meaningful change can take place. By “public relationship,” I don’t mean a warm and fuzzy embrace; I mean a thorny, knotty, often tension-filled relationship.

Both on the left and the right, this step has been forgotten, rejected or just plain missed. Both extremes act not to get into relationship with others who don’t agree with them, but to get their own narrow political bases to react and respond. Today liberals applaud the players and enjoy the discomfort of moderates and conservatives, while conservatives applaud each Trump tweet because it drives progressives to distraction.

As Alinsky wrote: “There are rules for radicals who want to change their world; there are certain central concepts of action in human politics that operate regardless of the scene or the time. To know these is basic to a pragmatic attack on the system. These rules make the difference between being a realistic radical and being a rhetorical one.”

If the NFL players want to be realistic radicals, they should think about two questions. With whom do they need to connect to help address their concerns? And how can they break the problem of police-community conflict into specific issues that can be corrected?

My advice to the players: You’ve run your action, gotten your reactions and are already, as athletes, recognized. Now is the time to identify key judges, prosecutors and police chiefs and to focus on proven ways to reduce the number of violent encounters between law enforcement and local residents.

Here’s one. Every cop in every city should do what the 36 police departments in Memphis and Miami-Dade County, Fla., do: provide comprehensive Crisis Intervention Team training for their officers. This equips police with the knowledge and tools to respond effectively to situations, especially when mental illness is a factor. In Miami-Dade, according to Steven Leifman, the judge in charge of the county’s courts and a jail diversion program, responding officers know how to divert troubled individuals to the facilities and the programs that can deal with their mental illness.

Out of 71,000 calls to 911 over a recent five-year period, only 150 arrests were made. The rest of the situations were calmly defused, and those who needed treatment received it. Before CIT training, there was a deadly shooting every month by police of individuals with mental illness. After the training there is less than one a year.

Officers have embraced this approach. They feel well-prepared and less exposed. They suffer fewer injuries and experience less stress. They earn the trust and gratitude of families and residents, not suspicion or hatred.

There are other specific and pragmatic changes that can and should be made, but they depend on NFL protesters to run a new play. It’s time to do the less dramatic work of forging relationships and identifying improvements that can begin to bring lasting peace and justice to our communities—saving thousands of precious lives.

Mr. Gecan is a co-director of the Chicago-based Industrial Areas Foundation.Appeared in the October 10, 2017, print edition.